University of Tabriz Computational Methods for Differential Equations 2345-3982 Articles in Press 2025 10 29 Modeling and Analysis of Dynamic Waveforms in Nonlinear Fractional Models of Fifth Order 20656 10.22034/cmde.2025.68014.3265 EN Muhammad Ashraf Department of Mathematics, CUI Vehari Campus, Vehari, Pakistan. Noor Muhammad School of Mathematics, Sichuan University, Chengdu 610065, China. Md. Abdullah Bin Masud Department of Mathematics, Jagannath University, Dhaka-1100, Bangladesh. Md. Nur Alam Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh. Md. Jakir Hossen Faculty of Engineering and Technology (FET), Multimedia University, Melaka-75450, Malaysia. Journal Article 2025 07 07 The overarching purpose of this work is to derive new exact traveling wave solutions for a fifth-order generalized nonlinear fractional differential<br />equation (5th-order GNFDE) by applying the Improved Auxiliary equation method. This equation is characterized by M-fractional derivatives (M-FD), which offer a larger basis for modeling complex dynamical systems with memory effects. The proposed methodology enables various types of solutions designed in the shape of traveling wave solutions, solitary wave solutions, and other prominent solution types, indicating the robustness and versatility of the approach in dealing with nonlinear fractional differential equations. Some investigated solutions are demonstrated in 2D and 3D graphics by smearing definite values to the parameters under constrained conditions to boost the key propagating features. The results contribute significantly to the development of analytical techniques for solving high-order nonlinear fractional differential equations (NLFDE). In addition, the method is efficient and applicable to various non-linear systems, further enhancing its practical efficacy. https://cmde.tabrizu.ac.ir/article_20656_a2621b27931c82a83434fd5d7d283faa.pdf